The opposition is launching an impassioned plea for urgent action to ban Nazi symbols but has been accused of a political stunt.
The push has come off the back of a protest in Melbourne which drew neo-Nazis, who used the Sieg Heil salute.
Liberal frontbencher Michaelia Cash said the push to ban the salute needed to take precedence.
"Every Australian should find the actions of that small group of protesters who dared to use the Nazi salute offensive," she told parliament.
"Those who display Nazi symbols or use the Nazi salute are either ignorant of the past or are deliberately promoting evil."
Finance Minister Katy Gallagher agreed there was no place in Australia for Nazi ideology.
"But I think we should also acknowledge this is a complex area of law and any move to ban Nazi symbols deserves serious consideration," she said.
"The Australian people deserve better. We should stand together, we should send a strong voice about the events we saw in Victoria.
"This bill needs serious consideration, not a stunt."
Tensions boiled over when Liberal senator Sarah Henderson cried in the chamber after an interjection from Labor minister Murray Watt.
The interjection related to text messages Senator Henderson reportedly sent to the Victorian Liberal leader in defence of the state MP he is trying to expel from the party for attending the Melbourne anti-transgender rights rally where Nazis showed up.
"I am disgusted in you," Senator Henderson yelled across the chamber.
Senator Watt withdrew the remarks.
Labor senators also took aim at Opposition Leader Peter Dutton for not strongly backing the push to expel state MP Moria Deeming.
Anthony Chisholm said there was a contrast in the actions of Victorian opposition leader John Pesutto moving to expel Ms Deeming, and the federal Liberals who had nine years in government to act.
"You can show leadership or you can pursue stunts. It is disappointing the federal Liberals have chosen stunts," the Labor senator said.
Liberal senator Anne Ruston said Labor was attacking the opposition over something "that could not be more important to humanity".
"Shame on you for not understanding how unbelievably painful this must be for so many Jews around the world, to think that you would suggest this is a stunt," she said.
"This is absolutely a matter of urgency."
The push to have the bill debated ultimately failed, despite all sides agreeing it was an important issue to discuss, with Labor, the Greens and One Nation voting down the suspension of standing orders.
Greens senator Sarah Hanson-Young expressed her anger at the push to have the legislation voted on almost immediately, saying politicising the issue would drag the debate into the gutter.
"I don't think anything we've displayed to the Australian people ... is anything to be proud of," she said during the debate.
"The politicking over this issue - which is serious, which is sensitive, which is fundamentally about the values of a respectful, democratic nation - should not be drawn into the gutter."